Abstract
We consider anti-plane motions of an elastic plate taking into account surface energy within the linear Gurtin-Murdoch surface elasticity. Two boundary-value problems are considered that describe complete shear dynamics of a plate with free faces or with free and clamped faces, respectively. These problems correspond to anti-plane dynamics of an elastic film perfectly or non-perfectly attached to a rigid substrate. Detailed analysis of dispersion relations is provided. In particular, the influence of the ratio of a plate thickness to characteristic length on the dispersion curves is analysed. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
| Original language | English |
|---|---|
| Article number | 20210373 |
| Journal | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences |
| Volume | 380 |
| Issue number | 2231 |
| DOIs | |
| State | Published - 5 Sep 2022 |
| Externally published | Yes |
Keywords
- anti-plane waves
- dispersion relations
- surface elasticity
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